2D and 3D data processing of archaeo-magnetic data

Introduction. The Sabine Necropolis at Colle del Forno (700-300 B.C.) at Montelibretti, Rome is characterized by dromos chamber tombs, most of them unexplored till now. The tombs can be assimilated to cavities of a standard volume of some cubic meters; the entrance of the tombs is a corridor 6 m long with a 1 square meter section . The surficial geology of the area consists of a series of tuffs about 10 m thick overlying Pleistocene-Quaternary sandy-clayey sediments. A thin layer of top soil (20 - 30 cm) covers the tuff. The investigation of the Necropolis in the past decade has been performed by different geophysical methodologies: electrical, electromagnetic and magnetic methods have been widely adopted to investigate several chamber tombs (Piro et al, 2001). The aim of this paper is to analyze an integrated approach to the processing of magnetic survey data. The magnetic susceptibility contrast between topsoil, subsoil and rocks (topsoil is normally more magnetic than subsoil) permits to detect ditches, pits and other silted-up features that were excavated and then silted or back-filled with topsoil. Meanwhile back-filled areas produce positive anomalies, less magnetic material introduced into topsoil, including many kinds of masonry (for example, limestone walls) may produce negative anomalies of the order of some nanoteslas. The same behavior is related to the presence of cultural voids and tombs whose magnetic anomaly is generated by the lack of magnetic materials due to the cavities of the tombs. In the area a diffused magnetisation is manly due to the presence of top soil and tuff materials and high negative susceptibility contrasts can be expected because of the presence of the tombs. The magnetic survey was performed along a regular grid of 0.5 m x 0.5 m using a optical pumped Caesium-vapour magnetometer G858 (Geometrics), in the gradient configuration, on an area which is well known as far as the presence, size and position of tombs are concerne

Sampling and Reconstruction of Sparse Signals on Circulant Graphs - An Introduction to Graph-FRI

With the objective of employing graphs toward a more generalized theory of signal processing, we present a novel sampling framework for (wavelet-)sparse signals defined on circulant graphs which extends basic properties of Finite Rate of Innovation (FRI) theory to the graph domain, and can be applied to arbitrary graphs via suitable approximation schemes. At its core, the introduced Graph-FRI-framework states that any K-sparse signal on the vertices of a circulant graph can be perfectly reconstructed from its dimensionality-reduced representation in the graph spectral domain, the Graph Fourier Transform (GFT), of minimum size 2K. By leveraging the recently developed theory of e-splines and e-spline wavelets on graphs, one can decompose this graph spectral transformation into the multiresolution low-pass filtering operation with a graph e-spline filter, and subsequent transformation to the spectral graph domain; this allows to infer a distinct sampling pattern, and, ultimately, the structure of an associated coarsened graph, which preserves essential properties of the original, including circularity and, where applicable, the graph generating set.Comment: To appear in Appl. Comput. Harmon. Anal. (2017

Equations of motion of slung load systems with results for dual lift

General simulation equations are derived for the rigid body motion of slung load systems. These systems are viewed as consisting of several rigid bodies connected by straight-line cables or links. The suspension can be assumed to be elastic or inelastic, both cases being of interest in simulation and control studies. Equations for the general system are obtained via D'Alembert's principle and the introduction of generalized velocity coordinates. Three forms are obtained. Two of these generalize previous case-specific results for single helicopter systems with elastic or inelastic suspensions. The third is a new formulation for inelastic suspensions. It is derived from the elastic suspension equations by choosing the generalized coordinates so as to separate motion due to cable stretching from motion with invariant cable lengths. The result is computationally more efficient than the conventional formulation, and is readily integrated with the elastic suspension formulation and readily applied to the complex dual lift and multilift systems. Equations are derived for dual lift systems. Three proposed suspension arrangements can be integrated in a single equation set. The equations are given in terms of the natural vectors and matrices of three-dimensional rigid body mechanics and are tractable for both analysis and programming

Accurate Complex Scaling of Three Dimensional Numerical Potentials

The complex scaling method, which consists in continuing spatial coordinates into the complex plane, is a well-established method that allows to compute resonant eigenfunctions of the time-independent Schroedinger operator. Whenever it is desirable to apply the complex scaling to investigate resonances in physical systems defined on numerical discrete grids, the most direct approach relies on the application of a similarity transformation to the original, unscaled Hamiltonian. We show that such an approach can be conveniently implemented in the Daubechies wavelet basis set, featuring a very promising level of generality, high accuracy, and no need for artificial convergence parameters. Complex scaling of three dimensional numerical potentials can be efficiently and accurately performed. By carrying out an illustrative resonant state computation in the case of a one-dimensional model potential, we then show that our wavelet-based approach may disclose new exciting opportunities in the field of computational non-Hermitian quantum mechanics.Comment: 11 pages, 8 figure